Did Shure manufactured a tri-polar microphone before the KSM44A?
Indeed we did. It was the model 720A, introduced in 1937. Like the KSM44A, the model 720A was switchable between "Non-Directional" (omnidirectional), "Uni-Directional" (cardioid), and "Bi-Directional" (figure-eight). The retail price was $39.50; in 2016 dollars, that would be $662.25.
The 720A had two crystal elements (one omnidirectional and one bidirectional); same for the KSM44A except the elements are condenser. The 720A crystal elements were employed under a licence from the Brush Development Company: Information about Brush
To create the cardioid pattern, the omnidirectional element is electronically combined with the bidirectional element.
From the 1937 literature: "Here for the first time is one microphone that does everything! The new Shure Tri-Polar Controlled Direction Crystal Microphone gives you all three basic directional characteristics in one microphone, each instantly available though a 3 point switch."
Two technical papers about the model 720A can be found here: Vintage Tech Bulletins
The brilliant Shure microphone engineer, Ben Bauer, wrote the following in his lab notebook, dated August 4 - 7, 1937: "These days were practically completely spent on specifications and claims of tri-polar cosine element patent. Good advancement has been made."
Below are advertising pages and a data sheet for the model 720A.